Question

There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. What is the probability of 4 stations detecting an enemy plane? Round your answer to nearest hundredth.

0.05

0.21

0.02

0.55

0.04

Answer 1

It is given that there are 5 radar stations. Now, let X be the number of stations detecting an enemy plane. We have to find the probability of 4 stations detecting an enemy plane. Thus, we have to find P(X = 4).

We will find out P(X = 4) using the binomial distribution formula which is :

P(X) = , where,

n = the number of trials which here is the number of radar stations,

x = total number of successes,

p = the probability of the success on individual trial which in this case is the probability of a single radar station detecting an enemy plane,

and , q = 1 - p.

Thus, from the above, we have,

n = 5, p = 0.55, q = 1 - 0.55 = 0.45, x = 4.

Thus, from the formula,

P(4) = [since, ]

= 5*(0.092)*(0.45) = 0.207

Thus, the required probability is 0.207.